Problem: What is the sum of the integers from $-30$ to $50$, inclusive?
Answer: The sum of the integers from $-30$ to 30 is zero, so we need to find only the sum of the integers from 31 to 50.

The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms.  The number of integers from 31 to 50 is $50 - 31 + 1 = 20$, so the sum is $(31 + 50)/2 \cdot 20 = \boxed{810}$.